Rational Adjustment of Imbalances in
Plant Survey Data
PAUL M. BERTHOUEX, Assistant Professor
JON SCHELLPFEFFER, Graduate Student
Department of Civil & Environmental Engineering
University of Wisconsin
Madison, Wisconsin
INTRODUCTION
Observation, measurement and data analysis are very important in sanitary
engineering because complex waste treatment problems are not solved by theory alone.
Sampling surveys provide data intended for use in problems involving estimation of waste
production, materials recovery, estimation of process parameters, and process control.
Unfortunately, natural variability and non-homogeneity of wastes create sampling
problems. Als.o, some measures of waste characteristics, such as BOD, are not very precise.
The result is that, after a sampling survey, engineers often reach the decision making stage
encumbered with a set of inconsistent data.
Sometimes errors and inconsistencies make the raw data unfit for use. The engineer
then needs to adjust the raw data and work with derived data that are consistent and better
suited for the intended purpose. Consider for example a situation where several flows have
been measured, as given in Figure 1, but the measured values do not satisfy the mass balance
relations imposed by the real world, that is. mass in equals mass out. The measured total
inflows exceed the measured outflow by four; the mass balance using the first four flows
also has a discrepancy of four units.
Q, = 21
02 ■ 35
N
V  °3 ' l0
Q5> 16
04 = 62
>  °6=2°
a,a98
ALL     FLOWS
MEASURED
CONSTRAINTS    (I)   Q,+02 +  Oj   - Q4     "0
(2)   Q4+Q5 + Q6 -07     -0
MEASURED        (I)      21+35+10-62   •A
12)   62+16 + 20-98=0 Figure I-     Typical survey imbalance.
Using the inconsistent raw data is not appealing; neither is making an arbitrary data
adjustment. The purpose of this paper is to present a rational method of altering, or
adjusting, the measured values to bring them into agreement with physical constraints. In
this case the data should be adjusted to satisfy the two mass balance relations. Furthermore,
the adjustment should be done so that the most reliable measurements receive the smallest
correction. The adjustment procedure proposed is the method of least squares, a common
sense procedure that has certain computational advantages. The computations are
considered after a generalized discussion of data adjustment problems.
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